Dark radiation and Decaying Matter
Viviana Niro
University of Barcelona
Beijing, 13 September, 2012
in collaboration with M. C. Gonzalez-Garcia and J. Salvado (work in progress)
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
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Outline
1
Introduction
2
Dark radiation and Dark Matter
Decaying Dark Matter
Non-thermal Dark Matter
3
Decaying Matter into neutrinos
Analytic study
Numerical study
4
Conclusions
V. Niro (University of Barcelona)
Dark radiation and decM
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Introduction
Dark radiation
In recent years, data on CMB has brought cosmology into a precision science and
have revealed a Universe made by roughly 23% of Dark Matter (DM) and 73% of
Dark Energy (DE)
At present, data from the Wilkinson Microwave Anisotropy Probe (WMAP)
collaboration, the Atacama Cosmology Telescope (ACT) and the South Pole
Telescope (SPT) have revealed hints towards the presence of an extra relativistic
weakly interacting component, usually called “dark radiation”
The radiation content of the Universe is parametrized as
"
1/3 #
7
4
ργ ,
ρrad = 1 + Neff
8
11
with ργ = (π 2 /15)Tγ4 . For the standard case of three active neutrino flavours:
SM
= 3.046, considering the effects of neutrino oscillations, incomplete neutrino
Neff
decoupling and QED corrections to the electromagnetic plasma.
V. Niro (University of Barcelona)
Dark radiation and decM
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Introduction
Dark radiation
The current constraints on Neff at 68% C.L. at CMB time are:
K. N. Abazajian et al., arXiv:1204.5379 [hep-ph]
Neff = 4.34+0.86
−0.88
WMAP7+BAO+H0 ,
Neff = 3.86 ± 0.42
WMAP7+SPT+BAO+H0 ,
Neff = 3.89 ± 0.41
WMAP7+ACT+SPT+BAO+H0 .
All data above hint towards an extra radiation species.
The number of active neutrinos is constrained by measurements of the decay width of
the Z boson to be 2.984 ± 0.008 → several authors invoked the presence of a sterile
neutrino to explain the above data, also in the light of short-baseline (SBL) neutrino
experiments, that favour one or two sterile neutrinos.
The value of Neff at the time of big bang nucleosynthesis (BBN) can be constrained
using primordial nucleosynthesis yields of deuterium and helium → ∆Neff < 1 at
95% C.L. at BBN time, independently of measurements on the baryon density from
CMB anisotropy data and of the neutron lifetime input.
G. Mangano and P. D. Serpico, arXiv:1103.1261 [astro-ph.CO]
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Dark radiation and decM
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Dark radiation and Dark Matter
Decaying Dark Matter
Decaying Dark Matter
The DM decay rate into neutrinos is tightly constrained: Γ−1
dec & 100 Gyr, using the CMB
anisotropy spectrum, weak lensing observations, Type Ia supernova data (SNIa), large
scale structure (LSS) and Lyman-α data.
S. De Lope Amigo, W. M. -Y. Cheung, Z. Huang and S. -P. Ng, arXiv:0812.4016 [hep-ph]
Decaying Dark Matter (DDM) alters the time of matter-radiation equality, and thus the
early integrated Sachs-Wolfe effect, with an increase in the first CMB peak. DDM also
changes the late integrated Sachs-Wolfe effect, with a direct consequence on the CMB
anisotropy spectrum at small multipoles.
Ωcdm
0.3
0.25
0.2
0
0.005
0.01
Γ/Gyr
V. Niro (University of Barcelona)
0.015
-1
Dark radiation and decM
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Dark radiation and Dark Matter
Decaying Dark Matter
Decaying Dark Matter
Considering a DM decay rate that depends on time, Γ = αH, where α is a constant and
H is the Hubble rate, an increase of ∆Neff ∼ 1 at CMB time can be obtained within this
framework. O. E. Bjaelde, S. Das and A. Moss, arXiv:1205.0553 [astro-ph.CO]
A 2σ upper-limit of α < 0.027 for WMAP+ACT and α < 0.028 for WMAP+SPT.
V. Niro (University of Barcelona)
Dark radiation and decM
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Dark radiation and Dark Matter
Non-thermal Dark Matter
Non-thermal Dark Matter
If a small fraction of the DM is produced through the decays of much heavier states, it
can alter the expansion history of the Universe in a similar way to an additional light
neutrino species. D. Hooper, F. S. Queiroz and N. Y. Gnedin, arXiv:1111.6599 [astro-ph.CO]
Considering the free-streaming lenght of non-thermally generated DM particles
→ scenarios in which most of the DM is cold, while a small fraction f is hot.
τ 1/2 m ′
mX
X
∆Neff ≃ 4.8 × 10−3
−
2
f
+
106 s
mX
mX ′
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
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Decaying Matter into neutrinos
Analytic study
Decaying matter into neutrinos
The decay of non-relativistic matter into radiation can provide the necessary increase in
Neff to resolve the conflict with the standard value of Neff = 3.046. Considering a
decaying matter (decM) with an energy density ρdec at t = 10−4 s, and a lifetime τ , the
increase in Neff after the decay is given by W. Fischler and J. Meyers, arXiv:1011.3501 [astro-ph.CO]
4/3 τ 1/2 ρdec [t = 10−4 s]
8
11
∆Neff =
7
4
10−4 s
ργ
ργ is the photon energy density at t = 10−4 s. A very rapid decay at t = τ is assumed.
V. Niro (University of Barcelona)
Dark radiation and decM
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Decaying Matter into neutrinos
Numerical study
Numerical study
A full numerical study of the decM scenario
Modification of the equations for the background and for the perturbations in the
CLASS code: R. J. Scherrer and M. S. Turner, Phys. Rev. D31 (1985), M. Lattanzi, arXiv:0802.3155 [hep-ph]
ρ̇dec
=
−3aHρdec − aΓdec ρdec ,
ρ̇dr
=
δ̇DM
=
δ̇R
=
θ̇R
=
σ̇R
=
Ḟl
=
−4aHρdr + aΓdec ρdec ,
1
− ḣ ,
2
2
4
ρdec
− ḣ − θR + aΓdec
(δDM − δR ) ,
3
3
ρR
ρdec
1
θR ,
δR − σR − aΓdec
k2
4
ρR
3
4
8
ρdec
1 8
σR ,
θR − kF3 +
ḣ + η̇ − aΓdec
2 15
5
15
5
ρR
ρdec
k
Fl ,
[lFl−1 − (l + 1) Fl+1 ] − aΓdec
2l + 1
ρR
where l ≥ 3 and F2 = 2σR . ρR ≡ ρν + ρdr , ρDM ≡ ρc + ρdec .
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Dark radiation and decM
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Decaying Matter into neutrinos
Numerical study
Numerical study
We include the results from WMAP7 on the temperature and polarization
anisotropies and the SPT data. WMAP: we use the likelihood function as provided
by the collaboration; SPT: we build the corresponding likelihood functions from
the data, covariance matrix and window functions
E. Komatsu et al., arXiv:1001.4538 [astro-ph.CO], R. Keisler et al., arXiv:1105.3182 [astro-ph.CO]
We introduce a Hubble parameter prior, based on the latest Hubble Space
Telescope value: H0 = 73.8 ± 2.4 km s−1 Mpc−1 . This measurement of H0 is
obtained from the magnitude-redshift relation of 240 low-z Type Ia supernovae at
z < 0.1.
A. G. Riess et al., arXiv:1103.2976 [astro-ph.CO]
We include the luminosity measurements of high-z SNIa as given by the
“Constitution” set, that consists of 397 supernovae
M. Hicken et al., arXiv:0901.4804 [astro-ph.CO]
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Dark radiation and decM
COSMO 2012
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Decaying Matter into neutrinos
Numerical study
Numerical study
We use the measurement of BAO scale obtained from the Two-Degree Field
Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey Data
Release 7 (SDSS DR7), using the two distance ratios dz ≡ rs (zd )/DV (z) at
z = 0.2 and z = 0.35
rs (zd ): the comoving sound horizon at the baryon drag epoch;
DV (z) = [(1 + z)2 DA2 cz/H(z)]1/3 , with DA the angular diameter distance.
W. J. Percival et al., arXiv: 0907.1660 [astro-ph.CO]
We introduce a prior for the value of Neff at BBN, T = 0.01 MeV, as obtained in
G. Mangano and P. D. Serpico, arXiv:1103.1261 [astro-ph.CO]
We also forced the decay to happen after neutrino decoupling, imposing that Neff
is equal to the standard value of 3.046 at T ≥ 1 MeV
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
11 / 16
Decaying Matter into neutrinos
Numerical study
MC Parameters
symbols
Cosmological constant density
Baryon density
Dark Matter density
Decaying Matter density
Scalar spectral index
Optical depth at reionization
Amplitude of scalar power spectrum at k = 0.05 Mpc−1
Decay rate
Sunyaev-Zel’dovich (SZ) amplitude
Amplitude of Poisson distributed point sources
Amplitude of clustered point sources
Ω̃Λ
Ω̃b
Ω̃c
log(Ω̃dec )
ns
τ
AS
log(Γdec /Gyr−1 )
SZ
PS
CPS
The last three parameters SZ , PS, CPS are nuisance parameter, that accounts for
foregrounds contributions to the SPT data set: the Sunyaev-Zel’dovich (SZ) amplitude,
the amplitude of Poisson distributed point sources and the amplitude of clustered point
sources. For these parameters, we used gaussian priors as given in E. Shirokoff et al.,
arXiv:1012.4788 [astro-ph.CO], R. Keisler et al., arXiv:1105.3182 [astro-ph.CO]
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
12 / 16
Decaying Matter into neutrinos
Numerical study
Analysis Parameters
symbols
Hubble constant today
Baryon density today
Dark Matter density today
Decaying Matter fraction at t = 10−4 s
Scalar spectral index
Optical depth at reionization
Amplitude of scalar power spectrum at k = 0.05 Mpc−1
Lifetime of decM
Effective number of relativistic degrees of freedom at t =
(tBBN , tCMB )
H0
Ωb h 2
Ωc h 2
log(ρdec /ργ )
ns
τ
AS
log(τdec /s)
BBN
(∆Neff
,
CMB
∆Neff )
The effective number of relativistic degrees of freedom is defined as
∆Neff ≡
at BBN and CMB time.
7
8
ρdec
4 4/3
11
ργ
.
Using the above data and the theoretical predictions for them, we construct the
corresponding combined likelihood function.
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
13 / 16
0.4
1200
60
800
40
0.2
400
0.1
0
72
74
78
76
H0@kmsMpcD
0
80
20
0.022
0.023
Wbh2
0
0.024
30
40
4
20
Prob
0
0.99
ns
1.01
2.2
2.4
2.6
AS ‰ 109
0.12
0.14
Wch2
10
0
0.06
0.10
Τ
8
1.2
6
Prob
0.8
0.4
0
2
0
0.97
Prob
6
Prob
60
20
Prob
Prob
Prob
Prob
0.3
4
Preliminary
2
1
2
CMB
DNeff
0
0
1
BBN
DNeff
Decaying Matter into neutrinos
Numerical study
logHΡdecΡΓ L
-4
95% C.L.
-6
Preliminary
-8
2
4
6
logHΤdecsL
8
10
The lifetime of the decM, τdec , ranges between 102 s and 1010 s
We found numerically the anti-correlation between the parameters log(ρdec /ργ )
and log(τdec /s)!
V. Niro (University of Barcelona)
Dark radiation and decM
COSMO 2012
15 / 16
Conclusions
Conclusions
Cosmological data present an hint for “dark radiation”
A number of theoretical model has been studied to explain this
additional relativistic degrees of freedom, including the possibility that
“dark radiation” could be produced from the decay into neutrinos of a
non-relativistic matter component
We have modified the CLASS code to conduct a full numerical study
for the case of decM into neutrinos, taking into account the
equations for the background and perturbations, as well as all the
relevant cosmological data
Note that the evidence for the increase in Neff is at the 2σ level. New
data are needed! The final answer will be obtained only from the data
of the Planck satellite, that will reach a precision in the measurement
of ∆Neff of the order of 0.26
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